Local time–space stochastic calculus for Lévy processes |
| |
Authors: | Nathalie Eisenbaum |
| |
Institution: | Laboratoire de Probabilités, UMR 7599, CNRS - Université Paris VI 4, Place Jussieu, 75252, Paris Cedex 05, France |
| |
Abstract: | We develop a stochastic calculus on the plane with respect to the local times of a large class of Lévy processes. We can then extend to these Lévy processes an Itô formula that was established previously for Brownian motion. Our method provides also a multidimensional version of the formula. We show that this formula generates many “Itô formulas” that fit various problems. In the special case of a linear Brownian motion, we recover a recently established Itô formula that involves local times on curves. This formula is already used in financial mathematics. |
| |
Keywords: | 60G44 60H05 60J55 60J65 |
本文献已被 ScienceDirect 等数据库收录! |
|